Monotonicity of entropy for real multimodal maps

Details Monotonicity of entropy for real multimodal maps Monotonicity of entropy for real multimodal maps

2009-05-20

arxiv.org/abs/0905.3377v1

Mathematics

Dynamical Systems

Scientific paper

In \cite{Mil}, Milnor posed the {\em Monotonicity Conjecture} that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected. This conjecture was proved for quadratic by Milnor & Thurston \cite{MT} and for cubic maps by Milnor & Tresser, see \cite{MTr} and also \cite{DGMT}. In this paper we will prove the general case.

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